Divergence and Projector Alignment

Historically, there have been different ways to set up stereoscopic projection as can be traced in the literature. Contemplated was dual projection using anaglyphs, or the polarized method for image selection. In one case, the projectors maintain a constant distance apart with the lens axes parallel. In the second case, the lens axes converge at the plane of the screen. In the first method there is no constancy with regard to placement of objects at the plane of the screen and that will change with the size of the screen, but background points can be set to remain at a fixed value no matter what size screen is used. The second method is the one we use when in fact the lens axes are coincidental.

The Real D system was not contemplated in the literature although it bears a close relationship to projection of single projector anaglyphs or Vectographs since the left and right lens axes for the Real D system are coincidental. One basic issue has to do with the constancy of the stereo effect or parallax as related to screen magnification. The amount of parallax is linearly proportional to the magnification.

In stereoscopic projection using the Real D system what can happen is that photography meant for one screen, when projected on a larger screen, can result in background points having divergence. All the parallax points will be increased linearly proportionally with respect to magnification; but may be of greatest concern will be the background points.

Divergence is a condition in which the vergence of the eyes is outward rather than inward. In the real world the condition of divergence does not occur, and eye muscles are not accustomed to fusing such images. Divergent parallax points have parallax greater than the interpupillary separation. Since there is quite a spread of interpupillary distances in the human population, say for children with about a two-inch separation to adults with a maximum of about a three-inch separation, we see that images created for one group may not work for another. In other words, if corresponding background points have a three-inch separation, then kids are going to be experiencing divergence–in fact, one that has an inch and a half of extra parallax–which may cause fatigue or eyestrain. Kids’ muscles may be more supple–anyway, that’s one hypothesis–so they may not have a problem viewing the images.

One approach, probably the one that makes the most sense, is to decide what the largest Real D screen is. Shoot for that, in terms of the background point parallax, and let everything else take care of itself. Let’s take the case of (I’m going to use round numbers here) Real D images that are meant for a 50-foot screen, which would be the outside limit of what we’re presently capable of doing; and let’s suppose that the creators of the images, either CGI or photographic images, decided on maximum positive parallax values of three inches for that 50-foot screen. When projected on a 25-foot screen, the maximum parallax for background points will be an inch and a half. The question is, how would those images look? When projected on a large screen, using the maximum parallax for background point, say three inches, you might expect that you’d get a deeper effect than on a smaller screen. Practically speaking, that’s not what happens and the image hold up–it looks fine. Even though the maximum background points would only be an inch and a half, and all other parallax values would be halved, on the 25-foot screen my experience is that the projected image still looks perfectly fine.

An important point to remember that sometimes gets overlooked is that, although screen parallax can be measured with a straight-edge ruler, in point of fact the most important way to look at parallax, in terms of view comfort, is its angular extent. Four inches of parallax when viewed from the front row is an entirely different matter for an observer sitting in the rear of the house. In other words, the retinal disparity in the front of the theater is going to be much greater than the resultant retinal disparity from the rear.

A rule of thumb for stereoscopic images is that you have to be kind and do no harm to the people in the front rows. (People who choose to sit in the front row are seeking as special experience for 2D or 3D projection.) You have to be considerate. But most of the people don’t sit in the front row so the photography really needs to take into account the visual effect for people who sit in the middle of the theater, where most people sit. It sounds like it may be a difficult problem to work out, but it really isn’t because it is possible to strike a balance.

The alternative to the recommendation I made above with regard to simply projecting–making no corrections in projection but with the filmmakers cognizant of the range of screens they’re going to use–would be to produce some kind of an offset in projection. It’s a relatively simple calculation because the parallax value is a linear function of magnification.

It’s also possible to laterally shift the images so that we have constant background parallax points, which is the first method described above for use with dual projectors. For Real D the method would be adapted to projection with a single machine and that will be possible with the next generation of TI projectors which will allow for horizontal pixel shifting. In this way we would, no matter what size screen, project and always have background points that are, say, t three inches apart. This is a technique that is used in IMAX. IMAX uses two projectors with an image offset that’s always the interpupillary distance for background points. I believe they recommend two-and-a-half inches for background points. In The Real D system we could also use these horizontal shifts. The problem with this approach is that, while we may be keeping the background points constant, we’re going to affect that which plays in the plane of the screen and the value of off-screen parallax points.

One of the most important things that needs to be considered at the time of photography or image generation is placement of objects in terms of the plane of the screen. If objects are placed at the plane of the screen they tend to be the easiest images to look at because they have the least crosstalk (the ghost image corresponds to itself) and the breakdown of convergence and accommodation is benign because accommodation and convergence correspond as they do in the visual field. If we make the correction that has been suggested, of image shifting, things may change for the worse. We’re going to be adding or subtracting parallax values to those image elements which would have appeared in the plane of the screen with values at or near zero parallax. In such a case these changes may produce problems in our desire to “fix” the background points. Shifting the images will result in adding to negative parallax (off-screen effects), which could change the ability to view images comfortably. Another matter that needs to be carefully considered are edge effects. If we are increasing negative parallax extent, or changing the parallax values at the vertical edges of the surround, we may be increasing difficulties with regard to viewing the image at the screen edges.

However, and this is a major point, shows shot with floating windows will work just fine with horizontal pixel shifting used to set up initial projection conditions to prevent divergence. That’s because the virtual window itself will simply have its parallax values adjusted automatically when the background points are shift to insure maximum comfort. For floating windows the plane of the screen becomes a virtual plane of the screen. It doesn’t really exist as a perceptual anchor since the physical screen surround is trumped by the virtual surround.

If a shot has background points that are the interpupillary separation for a small screen and we horizontally shift the image to keep that constant for a large screen we are going to move the entire image forward toward the audience adding to all parallax points because of this shift and because of the increased magnification. That might not work well without floating windows because of the conflict of vertical surround cues that might be created.

If a shot has background points that have the interpupillary separation for a large screen and we horizontally shift the image to keep that constant for a small screen we are going to move the entire image backward away from the audience subtracting from all parallax points because of this shift and because of the decreased magnification. That might not work too well either but it will be relatively benign because of the decreased magnification.

My recommendation is that we leave this thing alone until we consider these variables and we’re able to make a recommendation as a filmmaking community. You can’t do a test on one screen. We would need to take material that was specially prepared–worst-case material, let’s say–and project it on big and small screens. For example, we could go to Mann’s or the Bridge with test images and compare them, and see how they looked in the Clarity Theater. This is not necessarily going to be easy testing to do, because if you did a rigorous psychophysical test you’d have a number of test subjects, you’d show them targets, and so forth and so on. So, right now my recommendation is to do nothing and say nothing until we know what to do. We don’t want to create a problem by offering a solution that may not be valid, and may introduce more problems than it solves.

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